Explore BrainMass

Explore BrainMass

    Estimation: Sample size

    Not what you're looking for? Search our solutions OR ask your own Custom question.

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    A bank wants to estimate the mean dollars that each card holder will spend each month. It would like to be within plus or minus $10 of the true mean with a 98% confidence level. The standard deviation is thought to be $500. How many card holders should be sampled? After you've determined how many card holders should be sampled, the bank comes back and says that it will cost $5 per sample and they were only planning on spending $10,000 on the sample. In a memo to the bank product development team indicate how many card holders should be sampled to meet the original requirements of the sample. The explain the trade-offs that will occur when you lower the sample to $10,000 to meet their budget.

    © BrainMass Inc. brainmass.com December 24, 2021, 5:10 pm ad1c9bdddf
    https://brainmass.com/statistics/confidence-interval/estimation-sample-size-32415

    Solution Preview

    Standard deviation =σ= $500
    confidence interval= 98%

    This is a two tailed test since we are checking for both plus or minus $10
    Let the true mean be $μ
    What this problem is saying that we should be in the range $μ+10 and $μ-10 and

    With sampling we determine the confidence interval of $μ+Z σx and $μ-Z σx
    where
    Z is read from the normal probability distribution tables corresponding to ...

    Solution Summary

    Estimation-Sample size: The sample size for estimating the mean amount spent by card holders is calculated.

    $2.49

    ADVERTISEMENT